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Previous analysis of the vegetation cover from remote sensing revealed the existence of three alternative modes in the frequency distribution of boreal tree cover: a sparsely vegetated treeless state, an open woodland state, and a forest state. Identifying which are the regions subject to multimodality, and assessing which are the main factors underlying their existence, is important to project future change of natural vegetation cover and its effect on climate. We study the impact on the tree cover fraction distribution (TCF) of eight globally-observed environmental factors: mean annual rainfall (MAR), mean minimum temperature (MTmin), growing degree days above 0°C (GDD0), permafrost distribution (PZI), mean spring soil moisture (MSSM), wildfire occurrence frequency (FF), soil texture (ST), and mean thawing depth (MTD). Through the use of generalised additive models, conditional histograms, and phase-space analysis, we find that environmental conditions exert a strong control over the tree cover distribution, generally uniquely determining its state. Additionally, we find that the relationship between tree cover and environment is different within the four boreal regions here considered, namely Eastern North Eurasia, Western North Eurasia, Eastern North America, and Western North America. Furthermore, using a classification based on MAR, MTmin, MSSM, PZI, FF, and ST, we show the location of areas with potentially alternative tree cover states under the same environmental conditions in the boreal region. These areas, although encompassing a minor fraction of the boreal area (~5%), are of interest for a more detailed analysis of land-atmosphere interactions. [ABSTRACT FROM AUTHOR]