I can't understand Bait Shammai's reason why one may have food cook on Shabbos, have candles burning etc. if they hold "sheveesas kailov," - that one is mafkir his pots, candleholders etc. It seems very forced to me. When is this hefker in effect? Is it in effect all week or just Shabbos? Does anyone else but the baalim know about it? Would he be angry or makpid if someone came to take these hefker pots that he uses all the time? Doesn't there have to be some measure of real intention b'lav in his heart for hefker to take effect? If some one is mafkir whatever chometz he didn't find before Pesach (under the refridgerator, behind the sofa..) he probably wouldn't mind if someone took them. But the pots that he uses all the time? Could he possibly mean it?
(A) (1) TOSFOS (DH d'Mefakra) writes that "Mistama" he is Mafkir his items. That is, since the owner is required to be Mafkir his items because of the prohibition of Shevisas Keilim, we assume that he had in mind to be Mafkir them.
(2) The RASHBA writes that the concept of "Hefker Beis Din Havi Hefker" is coming into play here. That is, Beis Din has the right to be Mafkir anybody's property when they deem it necessary to do so. Hence, the owner does not need to be Mafkir his items himself; Beis Din does so automatically.
(3) The ROSH YOSEF asks the question that you asked -- that the owner's Hefker is not going to be done with full intention, and he answers that perhaps the owner verbally declares that his items are Hefker, and even though he does not really intend to make them Hefker, "Devarim she'b'Lev Einam Devarim" (thoughts in the heart do not count [when one's speech indicates otherwise]), and thus his explicit declaration overrides his unexpressed intention.
(b) It seems that being Mafkir these items is only temporary, and after Shabbos there is no need to do any act of acquisition to reclaim them, because they automatically revert to being his property. It also seems that when he is Mafkir them, he is only Mafkir them to Jews, but not to gentiles, and Beis Shamai is going according to his opinion elsewhere that such an act of being Mafkir works (Pe'ah 6). Consequently, while the items are Hefker to all Jews, no Jew can acquire them because it is forbidden to make an acquisition on Shabbos. No gentile can acquire them because they are not Hefker to gentiles. If so, the owner may indeed have full intention to be Mafkir his items, since he will only benefit from doing so (that is, no one can claim his items, and he will be permitted to benefit from the Melachah that those items perform on Shabbos).