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Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equationin unbounded domains, typically $\mathbb R_+$ 
or $\mathbb R^N$ 
. Considering an unbounded and disconnected control region of the form $\omega := \cup _n \omega _n$ 
, we prove two null controllability results:under some technical assumption on the control parts $\omega _n$ 
, we provethat every initial datum in some weighted L 2 space can be controlled to zero by usual control functions, and every initial datum in L 2(Ω) can be controlled to zero usingcontrol functions in a weighted L 2 space.At last we give several examples in which the control region has a finite measure and our null controllability results apply.
