
371 So.2d 145 (1979)
The TRAVELERS INSURANCE COMPANY, Appellant,
v.
Laurence H. WILSON, Appellee.
No. 78-809.
District Court of Appeal of Florida, Third District.
March 20, 1979.
*146 High, Stack, Lazenby & Bender and Alan R. Dakan, Miami, for appellant.
Horton, Perse & Ginsberg and Edward A. Perse, George P. Telepas, Miami, for appellee.
Before PEARSON, BARKDULL and HUBBART, JJ.
PER CURIAM.
The plaintiff, The Travelers Insurance Company, appeals a summary final judgment entered upon its complaint seeking a declaration that the insurance company was not liable for uninsured motorist coverage. The complaint prayed that the defendant, appellee here, Laurence H. Wilson, be "... temporarily and permanently [enjoined] from proceeding with his claim against the Plaintiff and bringing it before the American Arbitration Association . ." The summary judgment entered held that the plaintiff was not entitled to the injunction and ordered that the parties should proceed to arbitration.
Defendant Wilson is proceeding under the uninsured motorist provision of his automobile liability policy with The Travelers Insurance Company. Travelers' complaint alleged that Wilson was injured when his car was rear-ended by Francisco Mora (not a party to this action). Mora had liability insurance with limits of $15,000/$30,000, and Wilson had uninsured motorist coverage with Travelers in the same amount. Wilson sought arbitration under the uninsured motorist provision, contending that the tort-feasor was the driver of a phantom vehicle that made a sudden stop in front of him, causing his injuries.[1] During discovery, Travelers made a request for admission that Mora's negligence was at least, in part, responsible for the accident and for Wilson's injuries. Wilson answered that both Mora and the phantom vehicle were negligent and responsible.
The plaintiff Company moved for summary judgment upon the ground that:

*147 "... there is no genuine issue as to any material fact that the uninsured motorist coverage available to the Defendant is not greater than the liability limits provided under the State Farm policy issued to the third-party tort feasor, Mr. Francisco Mora and since the third-party tort feasor is a person jointly or severally liable together with the alleged uninsured phantom vehicle for the injuries allegedly sustained by the Defendant in the subject accident, the Defendant, is precluded from filing and maintaining an uninsured motorist claim or action against the Travelers Insurance Company ..."
It is well established that once either party to an insurance contract is successful in pleading a complaint for declaratory relief, the court becomes fully empowered and should completely adjudicate all the rights of the parties relating to coverage, liability and damages in order that the rights of the parties not be determined in a piecemeal fashion. Cruger v. Allstate Insurance Company, 162 So.2d 690 (Fla. 3d DCA 1964). See also Travelers Insurance Company v. Lee, 358 So.2d 88 (Fla. 3d DCA 1978); Tavares v. Allstate Insurance Company, 342 So.2d 551 (Fla. 3d DCA 1977); Perez v. State Automobile Insurance Association, 270 So.2d 377 (Fla. 3d DCA 1972); and Zeagler v. Commercial Union Insurance Company of New York, 166 So.2d 616 (Fla. 3d DCA 1964). Thus, the question remains whether the determination of issues of fact are necessary in order to enter a declaration upon the coverage question.
The relevant portion of the statute in force at the time of the subject collision is:
"(1) No automobile liability insurance covering liability arising out of the ownership, maintenance, or use of any motor vehicle shall be delivered or issued for delivery in this state with respect to any motor vehicle registered or principally garaged in this state unless coverage is provided therein or supplemental thereto for the protection of persons insured thereunder who are legally entitled to recover damages from owners or operators of uninsured motor vehicles because of bodily injury, sickness, or disease, including death, resulting therefrom... . The coverage provided under this section shall be excess over, but shall not duplicate the benefits available to an insured ... under any automobile liability or automobile medical expense coverages; or from the owner or operator of the uninsured motor vehicle or any other person or organization jointly or severally liable together with such owner or operator for the accident.
* * * * * *
"(3) For the purpose of this coverage, the term `uninsured motor vehicle' shall, subject to the terms and conditions of such coverage, be deemed to include an insured motor vehicle when the liability insurer thereof:
"(a) Is unable to make payment with respect to the legal liability of its insured within the limits specified therein because of insolvency; or
"(b) Has provided limits of bodily injury liability for its insured which are less than the limits applicable to the injured person provided under uninsured motorist's coverage applicable to the injured person." Section 627.727, Florida Statutes (1977)
The plaintiff insurer relies for reversal upon an interpretation of section (1), above quoted, to provide that where one of two joint tort-feasors has liability insurance in the same amount as the liability limits of an insured's uninsured motorist benefits, the insured may not recover uninsured motorist benefits even though the other tort-feasor is uninsured. For this interpretation, the plaintiff points to the language of the statute which is: "The coverage provided under this section shall be excess over, but shall not duplicate the benefits available to an insured ... under any automobile liability ... or [from] any other person or organization jointly or severally liable ..." The plaintiff urges that it is admitted upon the facts of this case that there is coverage "available" from Mora, who is at least jointly liable.
*148 Alternatively, the plaintiff maintains that if the liability or degree of liability of Mora is necessary for a determination of coverage, then the trial court should proceed to determine that issue under the rule that the fact issue is incidental to a determination of coverage.
The defendant's position is that whether a second tort-feasor was, in part, guilty of causing the accident is a totally irrelevant consideration because the defendant had an accident with an uninsured tort-feasor (i.e., the phantom vehicle). He buttresses his position with those cases which hold that the uninsured motorist statute is to be interpreted to give broad protection to the citizens of this state against uninsured motorists. See Salas v. Liberty Mutual Fire Insurance Company, 272 So.2d 1 (Fla. 1972).
We think that it is clear that the purpose of the legislature was to provide for broad coverage (i.e., not limited by special policy exclusions), but also carefully to exclude any duplication of benefits. Therefore, if the defendant recovers from Mora, whom he has already sued, he cannot recover under the uninsured motorist provision of his policy. In the posture of this case, the responsibility of Mora has not been determined.
The plaintiff insurer is not entitled to a judgment that coverage does not exist because there has been no determination of the fact that Mora is a tort-feasor. Although an interrogatory may properly seek an opinion concerning legal fault, the policy-holder's legal conclusion that both Mora and the phantom vehicle were at fault is not a basis for summary judgment on the question of coverage.
There is no provision of the law which requires a plaintiff to maintain only one suit against only one tort-feasor at a time. See Dulman v. Seaboard Coast Line Railroad Company, 308 So.2d 53 (Fla. 4th DCA 1975). Therefore, in response to Traveler's demand for a decision on the coverage question, he is entitled to show the existence of an uninsured vehicle which he claims caused the accident. The trial court may proceed to determine the factual question presented as an incident to the existence of coverage. If the trial court finds that there was no phantom vehicle, there would be no uninsured motorist coverage in this case. If the trial court finds that there was a phantom vehicle, it should abate this action pending the outcome of the previously-filed suit against Mora. If the plaintiff recovers the full amount of Mora's policy limits in that suit, there would be no uninsured motorist coverage in this case. Only if the plaintiff recovers nothing or less than Mora's policy limits in that suit would there be uninsured motorist coverage in this case; in any event, the plaintiff's total recovery from Mora and Travelers could not exceed the policy limits of the uninsured motorist coverage. Accordingly, the summary judgment appealed is reversed and the cause remanded for further proceedings in accordance with the views herein expressed.
Reversed and remanded.
NOTES
[1]  When the declaratory action was filed. Wilson had already brought a suit against Mora, the motorist whose car struck Wilson's car in the rear.
